Shortwave radiation parameterization scheme for subgrid topography

Topography is well known to alter the shortwave radiation balance at the surface. A detailed radiation balance is therefore required in mountainous terrain. In order to maintain the computational performance of large-scale models while at the same time increasing grid resolutions, subgrid parameterizations are gaining more importance. A complete radiation parameterization scheme for subgrid topography accounting for shading, limited sky view, and terrain reflections is presented. Each radiative flux is parameterized individually as a function of sky view factor, slope and sun elevation angle, and albedo. We validated the parameterization with domain-averaged values computed from a distributed radiation model which includes a detailed shortwave radiation balance. Furthermore, we quantify the individual topographic impacts on the shortwave radiation balance. Rather than using a limited set of real topographies we used a large ensemble of simulated topographies with a wide range of typical terrain characteristics to study all topographic influences on the radiation balance. To this end slopes and partial derivatives of seven real topographies from Switzerland and the United States were analyzed and Gaussian statistics were found to best approximate real topographies. Parameterized direct beam radiation presented previously compared well with modeled values over the entire range of slope angles. The approximation of multiple, anisotropic terrain reflections with single, isotropic terrain reflections was confirmed as long as domain-averaged values are considered. The validation of all parameterized radiative fluxes showed that it is indeed not necessary to compute subgrid fluxes in order to account for all topographic influences in large grid sizes.